WO2018188276A1 - Error modeling method for tail-end space curve trajectory of six-degree-of-freedom robot - Google Patents

Abstract

An error modeling method for a tail-end space curve trajectory of a six-degree-of-freedom robot. The method comprises the following steps: 1) selecting N path points on a space curve, N being determined by a specific operation task, and obtaining a linear displacement or an angular displacement of each joint on the basis of an inverse kinematic model; 2) choosing an interpolation algorithm for interpolation operation to obtain a function relation between each joint variable and time, taking a point every 20 ms to obtain M joint variables, and letting total movement time obtained by the interpolation algorithm be T(s), then M=(T/0.02; 3); 3) considering a structural error of each joint of a robot, and obtaining M corresponding trajectory points Q of the tail end of the robot by means of positive solution; 4) taking a point P on an ideal trajectory curve, so that Q is a point on a normal pass through the point P, thereby defining a trajectory error E to be the distance between the points P and Q, transforming the problem into a known ideal space trajectory curve equation and coordinates of the point Q, and calculating the error E; when E is approximately infinitesimal, the planned trajectory coinciding with the ideal trajectory; and 5) obtaining a tangent equation of the point P according to the curve equation, and calculating coordinates of the point P in combination with condition PQ<b>⊥</b>PP1 (P1 is any point on the tangent) so as to obtain the error E. According to the method, both interpolation algorithm operation and the effect of the structural effort of each joint link are considered, and a simple and actual error model is established.

Description

An Error Modeling Method for End Space Curve Trajectory of Six Degrees of Freedom Robot Technical field

The invention belongs to the field of industrial robot end tracking error analysis, and relates to an end error model reflecting the deviation between a planned trajectory and an ideal trajectory. The model considers the influence of the interpolation algorithm and the joint link parameter error simultaneously, and can control the end tracking accuracy of the robot. Provide a certain theoretical basis.

Background technique

As one of the important performance indicators of industrial robots, end tracking accuracy has become an important research content. The modern end error control mainly adopts the closed-loop control method. Although the closed-loop control algorithm can effectively improve the positioning and repeat positioning accuracy, it relies heavily on the measurement accuracy of the joint sensor and the end sensor, and also seriously complicates the robot structure and makes the continuous The tracking accuracy control problem of the trajectory becomes extremely difficult. For the planning of the end continuous trajectory, there are two types, one is to interpolate in the operating space, one is to interpolate in the joint space, and in order to ensure the flexibility of each joint, the researchers will mostly reflect the ideal continuous trajectory curve. The inverse of the characteristic path point is interpolated into the joint space, which results in the influence of the interpolation algorithm parameter value on the end tracking accuracy. Secondly, in the actual industrial robot system, the link parameter error caused by the manufacturing and assembly There is also a large impact on the accuracy of the end tracking. Therefore, in order to control the tracking accuracy of the robot end, it is necessary to consider these two influencing factors. In order to compensate the end motion trajectory error to improve the tracking accuracy and avoid the complexity and uncertainty of real-time measurement in real-time compensation, it is necessary to perform offline prediction of the tracking error in the trajectory planning process. Therefore, the robot end tracking error model is established. important. In the process of establishing the error model, since it is generally equal time to take points in the end position of the plan, how to take the points on the ideal trajectory and make a difference can truly reflect the deviation between the planned trajectory and the ideal trajectory. The key issue to be solved.

Summary of the invention

The invention aims to provide an error modeling method for a six-degree-of-freedom robot end space curve trajectory. The main feature of this method is that it also considers the interpolation algorithm operation and structural error, and provides a simple and practical error model for the continuous trajectory tracking problem of the robot, which provides a theoretical basis for controlling the tracking accuracy.

The technical solution adopted by the present invention is an error modeling method for a six-degree-of-freedom robot end space curve trajectory, and the method comprises the following steps:

1) Select N path points on the space curve, N is determined by the specific operation task, and the displacement or angular displacement of each joint line is obtained based on the inverse solution model.

2) Using an interpolation algorithm to perform interpolation calculation to obtain the relationship between each joint variable and time, take a point every 20ms to obtain M joint variables, and set the total motion time obtained by the interpolation algorithm to T(s), then M =T/0.02.

3) Considering the structural error of each joint of the robot, the positive solution obtains M corresponding trajectory points Q at the end of the robot.

4) Take the point P on the ideal trajectory curve so that Q is a point on the normal line of the point P, thus defining the trajectory error E as the distance between the points P and Q, and transforming the problem into a known ideal space trajectory curve equation and The coordinates of the Q point are used to obtain the error E; when E approaches the infinity hour, the planned trajectory coincides with the ideal trajectory.

5) Calculate the tangent equation of P point according to the curve equation, and combine the condition PQ⊥PP ₁ (P ₁ is any point on the tangent line) to calculate the coordinates of point P, and obtain the error E.

Figure 1 is a schematic diagram of the space curve trajectory planning error.

The invention is characterized in that the interpolation algorithm operation and the influence of the joint link structure errors are considered at the same time, and a more realistic error model is established for the continuous trajectory tracking task of the six-degree-of-freedom industrial robot, thereby providing a theoretical basis for realizing trajectory tracking precision control. .

DRAWINGS

Figure 1 Schematic diagram of spatial curve trajectory planning error

detailed description

Step (1) to find the joint variable

Let the robot end space operation task curve equation be as follows,

N path points are uniformly taken on the curve, and the joint angular displacement θ of the arm is obtained by inverse solution.

Step (2) Interpolation operation for each joint variable

An interpolation algorithm is used to interpolate the joint variables, and the relationship between the i-th joint variable and the motion time is obtained as follows.

θ _i =f _i (t)

A function value is taken every 20 ms on the function curve obtained according to the above formula, thereby obtaining M displacement values θ _{i of} each joint, and M corresponding trajectory points Q are calculated by the forward kinematics model.

Step (3) Calculate the robot end track point

Since the end position of the robot is related to the displacement amount θ _{i of} each joint, and secondly, it is related to the parameters of the robot DH link, that is, the length a _{i of the member} , the torsion angle α _{i of the member} , the joint distance d _i and the joint rotation angle θ _i , so the robot is The positive kinematics model is expressed as follows.

Pos=g _st (θ _i , a _i , α _i , d _i , θ _i )

In fact, the robot link parameters will produce errors during the manufacturing and assembly process, and this error will greatly affect the positioning accuracy of the robot end. The actual link parameters are known as a _i +Δa _i , α _i + Δα _i , d _i + Δd _i , θ _i + Δθ _i , when considering the structural error of each joint of the robot, the robot end position can be expressed as

Pos(actual)=g _st (θ _i , a _i +Δa _i , α _i +Δα _i , d _i +Δd _i , θ _i +Δθ _i )

Where θ _i is obtained by interpolation, so the actual position of the end of the robot is also affected by the interpolation algorithm. By substituting the M corners θ _i of the joints into the above equation, M corresponding end position points Q (X, Y, Z) can be obtained.

Step (4) Calculate the error E

Let point P be a point on the trajectory of the ideal space curve, and point Q is on the normal line passing P point, P ₁ point is on the tangent line passing point P, then PQ⊥PP ₁ , and the space coordinate of each point is P(x ₀ , y ₀ , z ₀ ) and P ₁ (x ₁ , y ₁ , z ₁ ), which are true reflections of the deviation between the actual trajectory of the end and the ideal trajectory. The trajectory error E defined by this patent is the distance between the points P and Q. (When E approaches infinity, the planned trajectory coincides with the ideal trajectory).

The tangent equation over the P point on the curve obtained by the spatial curve function is as follows.

Taking xx ₀ = Δx, yy ₀ and zz ₀ can be obtained from the above formula, and the following conditions are satisfied.

Finally, the position of the P point (x ₀ , y ₀ , z ₀ ) can be obtained from the above equations, and the error E is defined as follows.

Claims (2)

1. An error modeling method for a six-degree-of-freedom robot end space curve trajectory, characterized in that the method comprises the following steps:

   1) Select N path points on the space curve, N is determined by the specific operation task, and the displacement or angular displacement of each joint line is obtained based on the inverse solution model;

   2) Using an interpolation algorithm to perform interpolation calculation to obtain the relationship between each joint variable and time, take a point every 20ms to obtain M joint variables, and set the total motion time obtained by the interpolation algorithm to T(s), then M =T/0.02;

   3) Considering the structural error of each joint of the robot, the positive solution obtains M corresponding track points Q at the end of the robot;

   4) Take the point P on the ideal trajectory curve so that Q is a point on the normal line of the point P, thus defining the trajectory error E as the distance between the points P and Q, and transforming the problem into a known ideal space trajectory curve equation and The coordinates of the Q point are used to obtain the error E; when E approaches the infinity hour, the planned trajectory coincides with the ideal trajectory;

   5) Calculate the tangent equation of P point according to the curve equation, and combine the condition PQ⊥PP ₁ (P ₁ is any point on the tangent line) to calculate the coordinates of point P, and obtain the error E.
2. The error modeling method for a six-degree-of-freedom robot end space curve trajectory according to claim 1, wherein:

   Step (1) to find the joint variable

   Let the robot end space operation task curve equation be as follows,

   

   N path points are uniformly taken on the curve, and the joint angular displacement θ of the arm is obtained by inverse solution;

   Step (2) Interpolation operation for each joint variable

   An interpolation algorithm is used to interpolate the joint variables, and the relationship between the i-th joint variable and the motion time is obtained as follows.

   θ _i =f _i (t)

   A function value is obtained every 20 ms on the function curve obtained according to the above formula, thereby obtaining M displacement values θ _{i of} each joint, and M corresponding trajectory points Q are calculated by the forward kinematics model;

   Step (3) Calculate the robot end track point

   Since the end position of the robot is related to the displacement amount θ _{i of} each joint, and secondly, it is related to the parameter of the robot DH link, that is, the length a _{i of the member} , the torsion angle α _{i of the member} , the joint distance d _i and the joint rotation angle θ _i , so the robot is The positive kinematics model is expressed as follows.

   Pos=g _st (θ _i , a _i , α _i , d _i , θ _i )

   In fact, the robot link parameters will produce errors during the manufacturing and assembly process, and this error will greatly affect the positioning accuracy of the robot end. The actual link parameters are known as a _i +Δa _i , α _i + Δα _i , d _i + Δd _i , θ _i + Δθ _i , when considering the structural error of each joint of the robot, the robot end position can be expressed as

   Pos(actual)=g _st (θ _i , a _i +Δa _i , α _i +Δα _i , d _i +Δd _i , θ _i +Δθ _i )

   Where θ _i is obtained by interpolation, so the actual position of the end of the robot is also affected by the interpolation algorithm; by substituting the M corners θ _i of the joints into the above equation, M corresponding end position points Q (X, Y, Z);

   Step (4) Calculate the error E

   Let point P be a point on the trajectory of the ideal space curve, and point Q is on the normal line passing P point, P ₁ point is on the tangent line passing point P, then PQ ⊥ PP ₁ , and the space coordinates of each point are P (x ₀ , y ₀ , z ₀ ) and P ₁ (x ₁ , y ₁ , z ₁ ), which are true reflections of the deviation between the actual trajectory of the end and the ideal trajectory, and define the trajectory error E as the distance between the points P and Q. E approaches infinity hours, and the planned trajectory coincides with the ideal trajectory;

   The tangent equation over the P point on the curve obtained by the spatial curve function is as follows.

   

   Taking xx ₀ = Δx, yy ₀ and zz ₀ can be obtained from the above formula, and the following conditions are satisfied.

   

   Finally, the position of the P point (x ₀ , y ₀ , z ₀ ) can be obtained from the above equations, and the error E is defined as follows.

   

Images